How do you express $f (x) = \frac{3 x + 2}{(x - 1) (x + 4)}$ $f(x) = (3x + 2) / [(x - 1)(x + 4)]$ in partial fractions?

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Answer 1 · 2016-02-07T12:04:50

$\frac{3 x + 2}{(x - 1) (x + 4)} = \frac{1}{x - 1} + \frac{2}{x + 4}$ $(3x+2)/((x-1)(x+4))=1/(x-1)+2/(x+4)$

$\frac{3 x + 2}{(x - 1) (x + 4)} = \frac{A}{x - 1} + \frac{B}{x + 4}$ $(3x+2)/((x-1)(x+4)) = A/(x-1)+B/(x+4)$

$\Rightarrow 3 x + 2 = A (x + 4) + B (x - 1)$ $=> 3x+2 = A(x+4) + B(x-1)$

$\Rightarrow 3 x + 2 = (A + B) x + 4 A - B$ $=> 3x+2 = (A+B)x +4A-B$

$=>{(A+B=3),(4A-B=2):}$

$=>{(A=1),(B=2):}$

$:.(3x+2)/((x-1)(x+4))=1/(x-1)+2/(x+4)$

How do you express f(x) = (3x + 2) / [(x - 1)(x + 4)]f(x)=3x+2(x−1)(x+4) f(x) = (3x + 2) / [(x - 1)(x + 4)] in partial fractions?